Directional Newton methods in 𝑛 variables

Levin, Yuri; Ben-Israel, Adi

doi:10.1090/S0025-5718-01-01332-1

Directional Newton methods in $n$ variables
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by Yuri Levin and Adi Ben-Israel;

Math. Comp. 71 (2002), 251-262

DOI: https://doi.org/10.1090/S0025-5718-01-01332-1

Published electronically: May 17, 2001

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Abstract:

Directional Newton methods for functions $f$ of $n$ variables are shown to converge, under standard assumptions, to a solution of $f(\mathbf {x})=0$. The rate of convergence is quadratic, for near-gradient directions, and directions along components of the gradient of $f$ with maximal modulus. These methods are applied to solving systems of equations without inversion of the Jacobian matrix.

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